Related papers: A convex duality method for optimal liquidation wi…
In this article we develop a duality principle and concerning computational method for a structural optimization problem in elasticity. We consider the problem of finding the optimal topology for an elastic solid which minimizes its…
Optimal execution of portfolio transactions is the essential part of algorithmic trading. In this paper we present in simple analytical form the optimal trajectory for risk-averse trader with the assumption of exponential market recovery…
We study the problem of optimal dividend payout from a surplus process governed by Brownian motion with drift under the additional constraint of ratcheting, i.e. the dividend rate can never decrease. We solve the resulting two-dimensional…
We consider the problem of optimizing a portfolio of financial assets, where the number of assets can be much larger than the number of observations. The optimal portfolio weights require estimating the inverse covariance matrix of excess…
We consider the multi-period portfolio optimization problem with a single asset that can be held long or short. Due to the presence of transaction costs, maximizing the immediate reward at each period may prove detrimental, as frequent…
This paper studies four trading algorithms of a professional trader at a multilateral trading facility, observing a realistic two-sided limit order book whose dynamics are driven by the order book events. The identity of the trader can be…
In this paper we explore optimal liquidation in a market populated by a number of heterogeneous market makers that have limited inventory-carrying and risk-bearing capacity. We derive a reduced form model for the dynamic of their aggregated…
We propose a framework to study the optimal liquidation strategy in a limit order book for large-tick stocks, with spread equal to one tick. All order book events (market orders, limit orders and cancellations) occur according to…
We consider rate swaps which pay a fixed rate against a floating rate in presence of bid-ask spread costs. Even for simple models of bid-ask spread costs, there is no explicit strategy optimizing an expected function of the hedging error.…
In this paper we address the problem of optimal liquidation of a large portfolio composed by securities exposed to default risk. The default time is described in terms of a Brownian motion representing the evolution of the value of the…
We consider an investor that trades continuously and wants to liquidate an initial asset position within a prescribed time interval. During the execution of the liquidation order the investor is subject to execution risk. We study the…
Optimal control problems involving hybrid binary-continuous control costs are challenging due to their lack of convexity and weak lower semicontinuity. Replacing such costs with their convex relaxation leads to a primal-dual optimality…
We study the optimal behavior of a bidder in a real-time auction subject to the requirement that a specified collections of heterogeneous items be acquired within given time constraints. The problem facing this bidder is cast as a…
Trading large volumes of a financial asset in order driven markets requires the use of algorithmic execution dividing the volume in many transactions in order to minimize costs due to market impact. A proper design of an optimal execution…
This paper considers a general convex constrained problem setting where functions are not assumed to be differentiable nor Lipschitz continuous. Our motivation is in finding a simple first-order method for solving a wide range of convex…
We consider a collection of derivatives that depend on the price of an underlying asset at expiration or maturity. The absence of arbitrage is equivalent to the existence of a risk-neutral probability distribution on the price; in…
We develop a dynamic trading strategy in the Linear Quadratic Regulator (LQR) framework. By including a price mean-reversion signal into the optimization program, in a trading environment where market impact is linear and stage costs are…
In this paper, we combine modern portfolio theory and option pricing theory so that a trader who takes a position in a European option contract and the underlying assets can construct an optimal portfolio such that at the moment of the…
We consider the hedging problem where a futures position can be automatically liquidated by the exchange without notice. We derive a semi-closed form for an optimal hedging strategy with dual objectives - to minimise both the variance of…
The aim of this paper is to design an efficient multigrid method for constrained convex optimization problems arising from discretization of some underlying infinite dimensional problems. Due to problem dependency of this approach, we only…